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Properties

Label 324.5.f
Level $324$
Weight $5$
Character orbit 324.f
Rep. character $\chi_{324}(55,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $188$
Sturm bound $270$

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Defining parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 324.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(270\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(324, [\chi])\).

Total New Old
Modular forms 456 196 260
Cusp forms 408 188 220
Eisenstein series 48 8 40

Trace form

\( 188 q + 2 q^{4} + O(q^{10}) \) \( 188 q + 2 q^{4} - 68 q^{10} + 4 q^{13} + 2 q^{16} - 30 q^{22} - 10746 q^{25} + 1020 q^{28} - 1976 q^{34} - 8 q^{37} + 9502 q^{40} - 18000 q^{46} + 28130 q^{49} - 1340 q^{52} + 8224 q^{58} + 4 q^{61} - 15292 q^{64} - 3582 q^{70} + 6808 q^{73} - 7140 q^{76} + 16960 q^{82} + 2504 q^{85} + 2310 q^{88} - 44484 q^{94} - 11276 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(324, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{5}^{\mathrm{old}}(324, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(324, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)